Both players have contracts until the end of the 2024 season, with English to be eligible for free agency should he remain unsigned by the conclusion of next year.
Products out of Western Australia, both English and Naughton have been tied to potential moves back to their home state in recent weeks amid reported interest from WA clubs, who are believed to be ready to pounce if either player holds off on confirming their future by the midway mark of next season.
West Coast are expected to be aggressive through the coming draft periods, however their interest in both English and Naughton has been bookmarked for 2024.
The Bulldogs have become accustomed to losing quality talent through recent exchange windows, with Beverdige hopeful the club can retain both of its key-position stars for the future.
"It's common, it's understandable, especially the boys from those states," Beveridge told reporters on Thursday.
"Teams might have low picks that they may want to use, but we're used to it. We're always intrigued.
"I look forward to seeing guys who have moved on from our club who we haven't been able to keep through various reasons like Patty Lipinksi, seeing him return to play for the Pies the other night, Josh (Dunkley) at Brisbane and Zaine (Cordy) over at St Kilda. There are lots of our guys who have headed off.
"But we're doing everything we can to make sure we are in a position to retain Tim, and I think Aaron has been spoken about as well.
"We'll just pull out all stops to make sure the boys know that we believe they belong here and it's our desire that it's their desire to want to stay."
Both English and Naughton are part of a strong key-position crop at Whitten Oval, with new recruit Rory Lobb and top two draft selections Jamarra Ugle-Hagan and Sam Darcy also calling the Bulldogs home.
The Dogs recruited key defender Jedd Busslinger with their first-round draft selection last year and could be in line to secure promising 200cm key forward Jordan Croft through this year's National Draft.
Croft, the son of former Bulldog Matthew, has been among this year's best performers in the Coates Talent League and booted three goals for Vic Metro last weekend against South Australia.